It's easier to win on the easy level simple because there are more days to complete the goal. I have won on medium and insane multiple times without buying the last hatchery. If I still feel like playing I choose to keep the farms and then I earn enough money to buy the last hatchery and purchase pets.
The strategy I use is to have 10 of each animal minus the magic geese and the red dragonfly's in the 3rd hatchery. I have 10 purple dragons, 10 ruby gryphons and 10 icebirds. I click on all the eggs I can and when I finally run out of time I simply sell all the eggs. It's a much safer bet than trying to hatch eggs and selling the resulting pet. In most cases you'll get more money from selling the eggs over hatching and selling pets.